Method for decoding a data signal

ABSTRACT

A turbo decoder is used in a method for blockwise decoding a data signal that is error protection coded at a transmitter and that is detected in a receiver. The turbo decoder includes two feedback symbol estimators. In order to calculate its output values, at least one of the symbol estimators executes, with reference to a data block being considered, a plurality of forward and/or backward recursions over subintervals of the data block.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of copending InternationalApplication No. PCT/DE01/00154, filed Jan. 15, 2001, which designatedthe United States and was not published in English.

BACKGROUND OF THE INVENTION FIELD OF THE INVENTION

The invention relates to a method for decoding a data signal that istransmitted via a radio channel and that is error protection coded usinga turbo code.

In communication systems, for example mobile radio systems, the signal(speech signal, for example) that will be transmitted is subjected toconditioning in a source coder of a channel coding unit. The channelcoding unit serves the purpose of adapting the signal that will betransmitted to the properties of the transmission channel. Effectiveerror protection is achieved in this case by specifically introducingredundancy into the signal that will be transmitted.

Binary, parallel-concatenated recursive convolutional codes aredesignated as so-called “turbo codes”. Turbo codes constitute a powerfulform of error protection coding, particularly in the case of thetransmission of large data blocks.

A turbo decoder is used in the receiver for the purpose of decodingturbo codes. A turbo decoder includes two individual convolutionaldecoders that are connected to one another in feedback fashion.

A distinction is made in the case of convolutional decoders betweensymbol estimators—which operate using a character-by-characteralgorithm—and sequence estimators. An MAP (maximum a posteriori) symbolestimator is a special form of a symbol estimator. Such an estimatoroperates using the so-called MAP (maximum a posteriori) algorithm. MAPsymbol estimators have the advantage that a bit error ratio that is aslow as possible can be achieved with you.

A turbo decoder with two recursively connected MAP symbol estimators isdisclosed in the book, representing the closest prior art, entitled“Analyse und Entwurf digitaler Mobilfunksysteme” [“Analysis and designof digital mobile radio systems”], by P. Jung, Stuttgart, B. G. Teubner,1997 on pages 343-368, in particular FIG. E.2. A turbo code interleaveris arranged between the two MAP symbol estimators.

In the case of a blockwise turbo code decoding, a decoded data symbol isestimated on the basis of input sequences of a finite number N of bits.N is denoted as the block size.

A recursion method is applied in each MAP symbol estimator in order tocalculate the decoded data values. The recursion method includes aforward recursion and a backward recursion. Both recursions are carriedout over the entire block length (that is to say from the first bit ofthe block up to the last bit of the block or from the last bit of theblock up to the first bit of the block).

This results in the requirement of buffering the result data obtainedfrom the recursions in the MAP symbol estimator. The MAP symbolestimator therefore requires a memory whose size is sufficient forstoring the result data of the forward recursion and the backwardrecursion with reference to at least one data block.

Consequently, a large storage requirement is required in the MAP symbolestimator (particularly in the case of the decoding of large data blocksin the case of which the particular advantages of turbo decoding come tobear).

This is disadvantageous, since the required memory size constitutes asubstantial cost factor in mobile stations.

SUMMARY OF THE INVENTION

It is accordingly an object of the invention to provide a method fordecoding a data signal that has been coded for error protection using aturbo code, which overcomes the above mentioned disadvantages of theprior art methods of this general type.

In particular, it is an object of the invention to provide a method fordecoding a data signal that has been coded for error protection using aturbo code in which the method requires an amount of memory space thatis as low as possible. In other words, the method permits theimplementation of cost-effective turbo decoders.

With the foregoing and other objects in view there is provided, inaccordance with the invention, a method for blockwise decoding a datasignal. The method includes steps of: in a transmitter, using a turbocode to error protection code the data signal; transmitting the datasignal using a radio channel; providing a receiver having a turbodecoder with two feedback symbol estimators; and using the turbo decoderto detect the data signal by having at least one of the symbolestimators execute a plurality of recursions in order to calculateoutput values for the data block. Each one of the plurality of therecursions is either a forward recursion over a subinterval of the datablock or a backward recursion over a subinterval of the data block.

In the inventive method, the forward recursion run previously carriedout in a blockwise fashion and/or the backward recursion run previouslycarried out in blockwise fashion are replaced by a plurality of forwardand backward recursion runs performed segment by segment (with referenceto a data block considered). The importance of this for calculating aspecific decoded output value of the MAP symbol estimator considered isthat instead of the rigid, blockwise recursions there is a need only fora forward and/or backward recursion over a suitably selectablesubinterval of the data block.

This substantially reduces the number of the result data that needs tobe buffered in the MAP symbol estimator considered, that is to say, itpermits a more cost-effective hardware structure.

A particularly preferred stipulation of the recursion interval limits isdefined in that each subinterval for a forward recursion is assigned,for a backward recursion, a subinterval which includes the subintervalfor the forward recursion. In addition, the calculation of the nthoutput value of the data block is based only on a forward recursion overthe subinterval including the nth data value and on a backward recursionover the assigned subinterval.

The length of a subinterval for the forward recursion is preferablybetween 10 and 30 data values, and is in particular 20 data values.

In order to reduce the signal processing outlay, the inventive methodcan advantageously be combined with a calculating method for determiningthe output values of the symbol estimators, which is based on asuboptimal MAP algorithm. A suboptimal MAP algorithm is a reduced outlayversion of the MAP algorithm that (by contrast with the MAP algorithm)admittedly does not render possible any maximum bit error ratio of theoutput values, but covers fewer computational steps. The combination(segment-by-segment recursion, suboptimal MAP algorithm) creates a turbodecoding method forming a compromise between the memory spacerequirement and the computational outlay that is decidedly favorable forpractical applications.

Other features which are considered as characteristic for the inventionare set forth in the appended claims.

Although the invention is illustrated and described herein as embodiedin a method for decoding a data signal, it is nevertheless not intendedto be limited to the details shown, since various modifications andstructural changes may be made therein without departing from the spiritof the invention and within the scope and range of equivalents of theclaims.

The construction and method of operation of the invention, however,together with additional objects and-advantages thereof will be bestunderstood from the following description of specific embodiments whenread in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of the air interface of a mobileradio system with a transmitter and a receiver;

FIG. 2 is a block diagram of a turbo coder for generating a turbo code;

FIG. 3 is a block diagram of the RSC convolutional coder illustrated inFIG. 2;

FIG. 4 is a block diagram of the turbo decoder illustrated in FIG. 1;

FIG. 5 is a schematic illustration for explaining the inventivesegment-by-segment forward and backward recursions when calculatingreliability information in a symbol estimator of the turbo decoder; and

FIG. 6 is a schematic illustration for explaining the computationalsteps that will be carried out to calculate a logarithmic a-posterioriprobability ratio.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the figures of the drawing in detail and first,particularly, to FIG. 1 thereof, there is shown a transmitter S and areceiver E of a mobile radio system. The transmitter S is included, forexample, in a base station, and the receiver E in a mobile station ofthe mobile radio system.

The transmitter S has a turbo coder TCOD, a modulator MOD and atransmitting antenna SA.

The turbo coder TCOD receives a digital input signal in the form of datasymbols (for example bits) u₁, u₂, . . . A finite sequence U=(u₁, u₂, .. . , u_(N)), including N input signal data symbols (bits) u_(n), n=1,2, . . . , N, is considered below on the basis of the blockwise coding.As previously mentioned, the number N is denoted as the block size.

The input signal carries an item of useful information to betransmitted, for example a speech message. It can be generated, forexample, via a microphone-amplifier-analog/digital converter circuitchain (not illustrated).

The turbo coder TCOD adds redundancy to the digital input signal for thepurpose of error protection coding. An error protection coded datasignal in the form of a sequence D including K data symbols (bits),D=(d₁, d₂, . . . , d_(K)) is present at the output of the turbo coder D.

The ratio N/K (number of input bits/number of output bits) is designatedas the code rate R_(c) of a coder.

A modulator MOD modulates the error protection coded data signal onto acarrier signal. The carrier signal modulated by the error protectioncoded data signal is spectrally shaped, in a way not illustrated, by atransmission filter and is amplified by a transmitter amplifier beforeit is emitted as the radio signal FS by the transmitting antenna SA.

The receiver E has a receiving antenna EA, a demodulator DMOD and aturbo decoder TDEC.

The receiving antenna EA receives the radio signal FS disturbed byenvironmental influences and interference with radio signals of othersubscribers, and feeds it to the demodulator DMOD.

The demodulator DMOD equalizes the received radio signal FS takingaccount of the signal interference suffered in the radio channel. Anequalized data signal provided at the output of the demodulator DMOD ispresent in the form of a symbol sequence {circumflex over(D)}=({circumflex over (d)}₁, {circumflex over (d)}₂, . . . ,{circumflex over (d)}_(K)), whose elements {circumflex over (d)}₁,{circumflex over (d)}₂, . . . , {circumflex over (d)}_(K) arecontinuous-value estimates of the data symbols d₁, d₂, . . . , d_(K) ofthe error protection coded data signal sequence D.

The equalized data signal is sent to the turbo decoder TDEC, at whoseoutput a decoded output signal sequence Û=(û₁, û₂, . . . , û_(N)) isprovided. The elements û₁, û₂, . . . , û_(N) of the decoded outputsignal sequence Û are hypotheses of the data symbols u₁, u₂, . . . ,u_(N) of the input signals at the transmitting end in the form ofdiscrete values from the symbol supply (for example 0,1) of the inputsignal.

The bit error rate is defined by the relative frequency of misestimatesu_(n)≠û_(n), n=1, 2, . . . It may not exceed a specific maximumpermissible value in the case of mobile radio applications.

For better understanding the invention, the generation of a turbo codeis first explained using FIG. 2 before describing an exemplaryembodiment of the inventive decoding method.

A turbo coder TCOD has two identical binary recursive systematicconvolutional coders RSC1 and RSC2, as they are known in codingtechnology. Connected to the input, upstream of the second recursivesystematic convolutional coder RSC2, is a turbo code interleaver ILwhich causes the coding to be performed in a blockwise fashion. Theoutputs of the two convolutional coders RSC1 and RSC2 are connected ineach case to a multiplexer MUX via puncturer PKT1 and PKT2,respectively. Furthermore a signal sequence X that is identical to thedigital input signal sequence U is fed to the multiplexer MUX.

FIG. 3 shows the design of a recursive convolutional coder using RSC1 asan example. The convolutional coder RSC1 has, on the input side, a firstadder ADD1 and a shift register, connected downstream of the first adderADD1, with, for example, three memory cells T. At its output, theconvolutional coder RSC1 provides a redundancy data sequence Y1=(y1 ₁,y1 ₂, . . . , y1 _(N)) that is formed by a second adder ADD2.

It is clear that a redundancy data symbol yl_(n) (n=1, 2, . . . , N)present at the output at a specific instant is a function of the currentinput data symbol u_(n) of the input signal sequence U and of the stateof the shift register. The state of the shift register is a function, inturn, of the last 3 input data symbols. The fallback depth L isdesignated as the number of data symbols (binary characters) that areavailable at ADD1 for combination, that is to say here L=4.

The design of the second convolutional coder RSC2 is identical to thedesign of the first convolutional coder RSC1. RSC2 provides a redundancydata sequence Y2=(y2 ₁, y2 ₂, . . . , y2 _(N)) at its output.

The unchanged input signal sequence U can be regarded as second outputof the first convolutional coder RSC1. That is to say from this point ofview, the first convolutional coder RSC1 includes a second output atwhich there is output the data sequence X whose elements x₁, x₂, . . . ,x_(N) are identical to the elements u₁, u₂, . . . , u_(N) of the inputsignal sequence U. A similar statement holds for the secondconvolutional coder RSC2, and a second output of the secondconvolutional coder RSC2, which is identical to the interleaved inputsignal sequence U. Coders with this property are designated generally assystematic coders.

Exactly two output data symbols x_(n) and y1 _(n) or x_(n) and y2 _(n)are then output per input data symbol u_(n) by each convolutional coderRSC1 and RSC2, respectively. Each convolutional coder RSC1, RSC2therefore has a coding rate of R_(c)=0.5.

The multiplexer MUX serves to set the coding rate of the turbo coderTCOD. In order also to achieve a coding rate of, for example, R_(c)=0.5for TCOD, the two redundancy sequences Y1 and Y2 are alternatelypunctured and multiplexed. The redundancy data sequence Y=(y1 ₁, y2 ₂,y1 ₃, y2 ₄, . . . , y1 _(N), y2 _(N)) resulting in this case issubsequently multiplexed alternately with the systematic data sequenceX. The error protection coded data signal yielded in the case of this(special) form of turbo coding therefore has the form of D=(x₁, y1 ₁,x₂, y2 ₂, x₃, y1 ₃, x₄, y2 ₄, . . . , x_(N), y2 _(N)) (N may be assumedto be an even number)

The convolutional coder RSC1 can be interpreted as a finite, clockedautomaton and can be described by a so-called trellis diagram with Mpossible states. The trellis diagram of the convolutional coder RSC1with a shift register of 3 cells has M=2³=8 nodes that correspond to thepossible states of the shift register. An (arbitrary) first state m thatgoes over into a second state m′ through the input of one input bit(u_(n)=0 or 1) is connected to this in the trellis diagram by aconnecting line. Each redundancy sub-sequence Y1 corresponds to aspecific path along connecting lines through the trellis diagram of theRSC1 coder.

Trellis diagrams for illustrating the states of coders are known andwill not be explained in more detail here.

The inventive decoding method is explained below with reference to theturbo decoder TDEC shown in FIG. 4.

The turbo decoder TDEC includes a first and a second demultiplexer DMUX1and DMUX2, a memory MEM, a first and a second convolutional decoder DEC1and DEC2, an interleaver IL, a first and a second de-interleaver DIL1and DIL2, and a decision logic device (threshold value decision element)TL.

The convolutional decoders DEC1 and DEC2 are symbol estimators.

The equalized data sequence:

-   -   {circumflex over (D)}=({circumflex over (x)}₁, ŷ1 ₁, {circumflex        over (x)}₂, ŷ2 ₂, {circumflex over (x)}₃, ŷ1 ₃, {circumflex over        (x)}₄, ŷ2 ₄, . . . , {circumflex over (x)}_(N), ŷ2 _(N)) fed to        the turbo decoder TDEC by the demodulator DMOD is split up by        the first demultiplexer DMUX1 into the equalized systematic data        sequence {circumflex over (X)} (detected version of the input        signal sequence U(=X)) and the equalized redundancy sequence Ŷ        (detected version of the redundancy sequence Y).

The second demultiplexer DMUX 2 splits up the equalized redundancysequence Ŷ into the two equalized redundancy subsequences Ŷ1 and Ŷ2(detected versions of the redundancy subsequences Y1 and Y2). Theequalized (estimated) versions of the data symbols x_(n), y1 _(n), y2_(n) occurring at the transmitting end are denoted by {circumflex over(x)}_(n), ŷ1 _(n), ŷ2 _(n), (n=1, 2, . . . , N).

Starting from the sequences {circumflex over (X)} and Ŷ1 and a feedbacksequence Z, the first decoder DEC1 calculates a sequence of reliabilityinformation Λl=(Λl (u₁), Λl (u₂), . . . , Λl (u_(N))).

Each element Λ1(u_(n)) of the sequence Λ1 is a continuous-valuedlogarithmic probability ratio for the uncoded data symbol u_(n) of theinput signal sequence U, $\begin{matrix}{{{\Lambda\quad 1( u_{n} )} = {\ln\{ \frac{P(  {u_{n} = {1{{\hat{X},{\hat{Y}1},Z}}}} ) }{P(  {u_{n} = {0{{\hat{X},{\hat{Y}1},Z}}}} ) } \}}};} & (1)\end{matrix}$where P(u_(n)=1|{circumflex over (X)}, Ŷ1, Z) and P(u_(n)=0|{circumflexover (X)}, Ŷ1, Z) respectively designate the conditional probabilitiesthat the data symbol u_(n) is equal to 1 or equal to 0 on condition thatthe sequences {circumflex over (X)}, Ŷ1, Z are observed. Theseconditional probabilities are “a-posteriori probabilities”, since theprobabilities of the uncoded data symbols (here: bits) u₁ to u_(N) onwhich an event (the detected sequences {circumflex over (X)}, Ŷ1, Z)which has occurred is based are deduced from this event.

The element Λ1(u_(n)) of the sequence of reliability information Λ1 arealso designated as LLRs (Log Likelihood Ratios).

The sequence of reliability information Λl is interleaved by theinterleaver IL and fed as an interleaved sequence of reliabilityinformation Λ1 _(I) to the second convolutional decoder DEC2. The secondconvolutional decoder DEC2 calculates an interleaved feedback sequenceZ_(I) and an interleaved sequence Λ2 _(I) from the interleaved sequenceof reliability information Λ1 _(I) and from the sequence Ŷ2.

The interleaved feedback sequence Z_(I) is de-interleaved by the firstde-interleaver DIL1 and yields the feedback sequence Z. The elements Λ2_(I) (u_(n)) of the sequence Λ2 _(I) are likewise continuous-valueda-posteriori probability ratios for the uncoded data symbols u₁ to u_(N)of the input signal sequence U, that is to say $\begin{matrix}{{\Lambda\quad 2_{I}( u_{n} )} = {\ln\{ \frac{P(  {u_{n} = {1{{{\Lambda 1}_{I},{\hat{Y}2}}}}} ) }{P(  {u_{n} = {0{{{\Lambda 1}_{I},{\hat{Y}2}}}}} ) } \}}} & (2)\end{matrix}$the notation already explained being used.

The sequence Λ2 _(I) is de-interleaved by the second interleaver DIL2and is fed as a de-interleaved sequence Λ2 to the decision logic deviceTL. The decision logic device TL determines a reconstructed data symbolû_(n)=0 for each element Λ2 (u_(n)) of the sequence Λ2 with a value≦0and a reconstructed data symbol (bit) u_(n)=1 for each element of Λ2with a value>0.

The mode of calculation of the LLRs Λ1 (u_(n)) and Λ2 _(I)(u_(n)) ischaracteristic of a turbo decoding method. The recursive calculation ofΛ1 is explained below.

The state of the convolutional coder RSC1 at the instant n (that is tosay in the case of the input data symbol u_(n)) is denoted by S_(N).

The conditional a-posteriori probabilities in equation 1 can beexpressed as sums of individual a-posteriori probabilities via the Mpossible states of the coder RSC1: $\begin{matrix}{{\Lambda\quad 1( u_{n} )} = {\ln\{ \frac{\sum\limits_{m = 1}^{M}\quad{P(  {{u_{n} = 1},{S_{n} = {m{{\hat{X},{\hat{Y}1},Z}}}}} ) }}{\sum\limits_{m = 1}^{M}\quad{P(  {{u_{n} = 0},{S_{n} = {m{{\hat{X},{\hat{Y}1},Z}}}}} ) }} \}}} & (3)\end{matrix}$

The individual probabilities can be written in the following form:

 P(u _(n) =i, S _(n) =m|{circumflex over (X)}, Ŷ1, Z)=α_(n)^(i)(m)·β_(n)(m) i=0, 1;

whereα_(n) ^(i)(m)=P(u _(n) =u, S _(n) =m|R ₁ ^(n)), and$\begin{matrix}{{\beta_{n}(m)} = {\frac{p( {{R_{n + 1}^{N}❘s_{n}} = m} )}{p( {R_{n + 1}^{N}❘R_{1}^{N}} )}.}} & (4)\end{matrix}$The sequence:R _(ν) ^(μ)=(R _(ν) , . . . , R _(μ)), 1≦ν<μ≦N  (5)consists of the three values R_(n)=(x_(n), yl_(n), z_(n)) of systematicinformation, redundancy information, and recursion information that aredefined in order to simplify the notation.

The expression α_(n) ^(i)(m) can be calculated by a forward recursion,and the expression β_(n)(m) can be calculated by a backward recursion.The expressions are therefore also designated as forward and backwardmetrics. A detailed description of the recursions (using an (optimum)MAP symbol estimation) is given in chapter E.3.3 “RekursiveMAP-Symbolschätzung” [“Recursive MAP symbol estimation”] of theabove-named book by P. Jung on pages 353 to 361. The recursions run overthe entire block, that is to say the forward recursion begins at theinstant 1 (first bit of the sequences {circumflex over (X)}, Ŷ1, Z) andends at the instant N (last bit of the sequences {circumflex over (X)},Ŷ1, Z) and the backward recursion begins at the instant N and ends atthe instant 1.

An exemplary embodiment of the inventive method that includes performinga plurality of subinterval recursion runs for calculating the LLRs fromequations (1), (3) is explained below with the aid of FIG. 5.

Let N=300, for example. Starting at n=0, first, for example, the first20 values α₀ ^(i)(m), . . . , α₁₉ ^(i)(m) are initially determined in afirst forward recursion run VR1, and are buffered in a forward recursionmemory area (not illustrated) of the convolutional decoder DEC1.

The associated first backward recursion RR1 begins here, for example, atn=79 and runs up to n=0. The corresponding values for β_(n)(m) arecalculated and buffered in a backward recursion memory area (notillustrated) of the convolutional decoder DEC1.

All 20 calculated values for α_(n) ^(i) (m) and the last twentycalculated values for β_(n)(m) are used in order to calculate the LLRsin the block segment n=0, 1, . . . , 19.

After the calculation of the first 20 LLRs, the two recursion intervals(recursion windows) are each displaced by 20 values. The second forwardrecursion VR2 therefore begins at n=20 and runs up to n=39. The resultdata obtained in the first forward recursion VR1 can be overwritten whenbuffering the values α₂₀ ^(i) (m), . . . , α₃₉ ^(i)(m). The associatedsecond backward recursion RR2 starts at n=99 and runs back to n=20. Theresult data determined in the first backward recursion RR1 can also beoverwritten here by the new data values β_(n)(m), n=99 to 20. In orderto calculate the LLRs in the block segment n=20, 21, . . . , 39, onceagain all 20 calculated values are used for α_(n) ^(i)(m) and the lasttwenty calculated values are used for β_(n)(m).

This segment-by-segment determination of the LLRs with floating forwardand backward recursion windows is continued in the way described untilall LLRs of the data block are calculated. Because of thesegment-by-segment mode of calculation, the dataset that must bebuffered during processing of a block segment is substantially reducedby comparison with the multi-block recursion runs used in the prior art.

Again, it is possible, and from the point of view of economizing memoryspace requirement, it is preferred to manage without a backwardrecursion memory area. In the case of such a hardware design, the LLRsof the respective block segment are calculated from the stored forwardrecursion values and the currently calculated backward recursion valuesdirectly (that is to say without buffering the latter).

The forward and backward recursions illustrated in FIG. 5 can begeneralized advantageously as follows: the length of the forwardrecursion window (here—20) is denoted by D(VR), and the length of thebackward recursion window (here: 80) is denoted by D(RR). The length ofthe backward recursion window is preferably determined in accordancewith the relationship D(RR)=L×D(VR), L being the fallback depth (in thepresent example, L=4).

Two possibilities of calculating the forward and backward recursionexpressions α_(n) ^(i)(m), β_(n)(m) are specified below.

According to a first, known possibility, that is described in detail onpages 353 to 361 in chapter E.3.3 “Rekursive MAP-Symbolschätzung”[“Recursive MAP symbol estimation”] of the abovenamed book by P. Jung,which is incorporated in this regard into the subject matter of thisdocument by reference, carrying out an MAP symbol estimation results in:$\begin{matrix}{{{\alpha_{n}^{i}(m)} = \frac{\sum\limits_{m^{\prime} = 1}^{M}\quad{\sum\limits_{j = 0}^{1}\quad{{\gamma_{n}^{i}( {R_{n},m^{\prime},m} )} \cdot {\alpha_{n - 1}^{j}( m^{\prime} )}}}}{\sum\limits_{m = 1}^{M}\quad{\sum\limits_{m^{\prime} = 1}^{M}\quad{\sum\limits_{k = 0}^{1}\quad{\sum\limits_{j = 0}^{1}\quad{{\gamma_{n}^{k}( {R_{n},m^{\prime},m} )} \cdot {\alpha_{n - 1}^{j}( m^{\prime} )}}}}}}},} & (6)\end{matrix}$i=0,1n=1, . . . , Nfor the forward recursion, and in: $\begin{matrix}{{{\beta_{n}(m)} = \frac{\sum\limits_{m^{\prime} = 1}^{M}\quad{\sum\limits_{j = 0}^{1}\quad{{\gamma_{n + 1}^{j}( {R_{n + 1},m,m^{\prime}} )} \cdot {\beta_{n + 1}( m^{\prime} )}}}}{\sum\limits_{m = 1}^{M}\quad{\sum\limits_{m^{\prime} = 1}^{M}\quad{\sum\limits_{k = 0}^{1}\quad{\sum\limits_{j = 0}^{1}\quad{{\gamma_{n + 1}^{k}( {R_{n + 1},m^{\prime},m} )} \cdot {\alpha_{n}^{j}( m^{\prime} )}}}}}}},} & (7)\end{matrix}$m=1, . . . M n=1, . . . , Nfor the backward recursion.

The expressions γ_(n) ^(i)(R_(n), m′,m) are the transition probabilitiesfrom a first state S_(n−1)=m′ into a second state S_(n)=m of the coderRSC1 in the trellis diagram, that is to say:γ_(n) ^(i)(R _(n) , m′, m)=P(u _(n) =i, S _(n) =m, R _(n) |S _(n−1)=m′)  (8).

A second possibility for calculating the forward and backward recursionexpressions α_(n) ^(i)(m), β_(n)(m) is specified below. As may be seenfrom the following equations, the computational outlay is substantiallyreduced in this second possibility in comparison with the firstpossibility: $\begin{matrix}{{{\alpha_{n}^{i}(m)} = {\sum\limits_{m^{\prime} = 0}^{M}\quad{\sum\limits_{j = 0}^{1}\quad{{\alpha_{n - 1}^{j}( m^{\prime} )} \cdot {\gamma_{n}^{i}( {R_{n},m^{\prime},m} )}}}}},} & (9)\end{matrix}$i=0,1, n=1, . . . , N; and $\begin{matrix}{{{\beta_{n}(m)} = {\sum\limits_{m^{\prime} = 1}^{M}\quad{\sum\limits_{j = 0}^{1}\quad{{\beta_{n + 1}( m^{\prime} )} \cdot {\gamma_{n + 1}^{j}( {R_{n + 1},m,m^{\prime}} )}}}}},} & (10)\end{matrix}$where m=1, . . . , M, n=1, . . . , N.

In contrast with the LLRs calculated using equations 6 and 7 (inconjunction with equations 1, 3 and 4) (1st possibility), it is not theratios of probabilities but the probabilities themselves that arecalculated directly in the recursions using equations 9 and 10 (2ndpossibility). This certainly leads to a decrease in the computationalaccuracy, but it is the substantially lower number of computationalsteps that is advantageous. The second possibility is therefore alsodesignated as suboptimal MAP symbol estimation.

FIG. 6 illustrates the summation over the M states of the coder RSC1,that must be carried out in order to calculate the 20 LLRs of a blocksegment extending from n=k to n=k+19 in accordance with the forwardrecursion equation (6) or (9) and the backward recursion equation (7) or(10).

In the case of the first forward recursion in a block (that is to saywhere k=0), all forward recursion expressions α₀ ^(i)(m) with theexception of the forward recursion expressions for the initial state m=1are initialized to the value 0. The initial state m=1 is known to thereceiver by prior agreement and is initialized correctly. In the case ofthe first backward recursion (k=0) in a block, no knowledge is availableon the backward recursion initial state, that is to say every possiblestate is equally probable. Consequently, all initial values β₈₀(m) areset to the value 1/M.

In the case of the second and all the following forward recursions, theforward recursion expressions obtained in the respectively precedingforward recursion are normalized and then used as initial values of thecurrent forward recursion. That is to say, the forward recursionexpressions are not built up on one another solely within one recursionwindow, but also with reference to successive recursion windows. Incontrast, in the case of the backward recursions (apart from the lastbackward recursion) the initial states are always unknown, that is tosay, the initial values for the backward recursions are always set to1/M. There is an exception only for the last backward recursion in ablock, since here the final state in the trellis diagram is known.

The backward recursion expressions (as initial values for the backwardrecursion following therefrom) do not have to be normalized because ofthe relatively small size of the backward recursion window by comparisonwith the overall possible length of the trellis diagram.

It becomes clear that all possible states of the coder RSC1 are takeninto account in calculating the LLRs in accordance with FIG. 6.

1. A method for blockwise decoding a data signal, which comprises: in atransmitter, using a turbo coder to error protection code the datasignal; transmitting the data signal using a radio channel; providing areceiver having a turbo decoder with two feedback symbol estimators;using the turbo decoder to detect the data signal by having at least oneof the symbol estimators execute a plurality of recursions in order tocalculate output values for a data block; and selecting each one of theplurality of the recursions from a group consisting of a forwardrecursion over a subinterval of the data block and a backward recursionover a subinterval of the data block, the plurality of the recursionsincluding a plurality of forward recursions over subintervals, thesubintervals for the plurality of the forward recursions covering thedata block completely, each of the subintervals for the plurality of theforward recursions being D(VR) data values long and the subinterval forthe backward recursion being D(RR) data values long, the data valuescorresponding to the formula: D(RR) =D(VR) x L, where L is a failbackdepth of a convolutional coder that is used to error protection code thedata signal.
 2. The method according to claim 1, wherein: eachsubinterval for a respective one of the plurality of the forwardrecursions is assigned a subinterval for the backward recursion thatincludes the subinterval for the respective one of the plurality of theforward recursions; and a calculation of an nth output value of the datablock is based only on one of the plurality of the forward recursionsover a subinterval including an nth data value and on a backwardtecursion over an assigned subinterval, wherein n is an interger value.3. The method according to claim 1, wherein: D(VR) lies between 10 and30.
 4. The method according to claim 1, wherein: D(VR) is
 20. 5. Themethod according to claim 1, which further comprises: in a recursionover a subinterval in a given direction, using calculated metrics of theturbo coder as initial values in a subsequent recursion of the givendirection.
 6. The method according to claim 1, which comprises: using asuboptimal MAP algorithm to calculate the output values of the at leastone of the symbol estimators.
 7. The method according to claim 1,wherein: each subinterval for a respective forward recursion is assigneda subinterval for the backward recursion that includes the subintervalfor the respective forward recursion; and a calculation of an nth outputvalue of the data block is based only on a forward recursion over asubinterval including an nth data value, and on the backward recursionover an assigned subinterval, wherein n is an integer value.